reserve m for Nat;
reserve P,PP,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem
  for s being State of SCM+FSA, I being Program of SCM+FSA st s.intloc 0
= 1 & Directed I is_pseudo-closed_on s,P
 holds DataPart IExec(I ";" Stop SCM+FSA,P,s)
  = DataPart Comput(P +* I, (Initialize s),
pseudo-LifeSpan(s,P,Directed I))
proof
  let s be State of SCM+FSA;
  set D = Data-Locations SCM+FSA;
  let I be Program of SCM+FSA;
  set I0 = Directed I;
  set I1 = I ";" Stop SCM+FSA;
  set s2 = Initialize s,
      P2 = P +* I;
  set s10 = Initialize s,
      P10 = P+*I1;
  set k = pseudo-LifeSpan(s,P,I0);
  assume
A1: s.intloc 0 = 1;
  assume
A2: I0 is_pseudo-closed_on s,P;
A3: s10 = Initialized s by A1,SCMFSA_M:18;
  thus DataPart IExec(I1,P,s)
     = DataPart(Result(P10,s10)) by A3
    .= DataPart Comput(P2, s2,k) by A2,Th22;
end;
